Quantum kinetic theory IV: Intensity and amplitude fluctuations of a Bose- Einstein condensate at finite temperature including trap loss

TL;DR

This paper employs quantum kinetic theory to analyze the steady state and fluctuations of a finite-temperature trapped Bose-Einstein condensate, including effects of trap loss, revealing detailed fluctuation dynamics and correlation functions.

Contribution

It introduces a quantum kinetic framework combining Bogoliubov and classical treatments to describe condensate fluctuations at finite temperature with trap loss effects.

Findings

Lorentzian line shape for intensity correlation function

Ballistic and diffusive regimes for amplitude fluctuations

Effect of particle loss on condensate stability

Abstract

We use the quantum kinetic theory to calculate the steady state and the fluctuations of a trapped Bose-Einstein condensate at finite temperature. The system is divided in a condensate and a non-condensate part. A quantum mechanical description based on the number conserving Bogoliubov method is used for describing the condensate part. The non-condensed particles are treated as a classical gas in thermal equilibrium with temperature T and chemical potential mu. We find a master equation for the reduced density operator of the Bose-Einstein condensate, calculate the steady state of the system and investigate the effect of one- two- and three particle loss on the condensate. Using linearized Ito equations we find expressions for the intensity fluctuations and the amplitude fluctuations in the condensate. A Lorentzian line shape is found for the intensity correlation function that is characterized by a time constant gammaI^(-1) derived in the paper. For the amplitude correlation function we find ballistic behavior for time differences smaller than gammaI^(-1) and diffusive behavior for larger time differences